HashMap and int as key

You can't use a primitive because HashMap use object internally for the key. So you can only use an object that inherits from Object (that is any object).

That is the function put() in HashMap and as you can see it uses Object for K:

public V put(K key, V value) {
    if (key == null)
        return putForNullKey(value);
    int hash = hash(key);
    int i = indexFor(hash, table.length);
    for (Entry<K,V> e = table[i]; e != null; e = e.next) {
        Object k;
        if (e.hash == hash && ((k = e.key) == key || key.equals(k))) {
            V oldValue = e.value;
            e.value = value;
            e.recordAccess(this);
            return oldValue;
        }
    }

    modCount++;
    addEntry(hash, key, value, i);
    return null;
}

The expression "k = e.key" should make it clear.

I suggest to use a wrapper like Integer and autoboxing.

You may try to use Trove http://trove.starlight-systems.com/
TIntObjectHashMap is probably what you are looking for.

For everybody who codes Java for Android devices and ends up here: use SparseArray for better performance;

private final SparseArray<myObject> myMap = new SparseArray<myObject>();

with this you can use int instead of Integer like;

int newPos = 3;

myMap.put(newPos, newObject);
myMap.get(newPos);

Use Integer instead.

HashMap<Integer, MyObject> myMap = new HashMap<Integer, MyObject>();

Java will automatically autobox your int primitive values to Integer objects.

Read more about autoboxing from Oracle Java documentations.